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In the last lesson we used the Law of Cosines to find the length of the third side of a triangle when you know the length of two sides and the angle in between. This law can also be used to find the measure of an angle when the three sides of a triangle are given. To use the Law of Cosines to find an unknown angle: 1. Identify c as the side across from the angle you are trying to find. 2. Substitute the values into the Law of Cosines.
Add the the sum of the angles in the triangle with two angles. For example, if you have a triangle inside a quadrilateral with the angles 45 and 20 degrees, you would get a sum of 65 degrees (20 + 45 = 65). Subtract the sum of the angles from 180 to get the third angle of the triangle. For example, if you have a triangle within a quadrilateral that has the angles 20 and 45 degrees you would get a third angle of 115 degrees (180 - 65 = 115). Add the two known angles of the quadrilateral with the new angle.